Solve for $x$ : $x^2 - 6x - 40 = 0$
Solution: The coefficient on the $x$ term is $-6$ and the constant term is $-40$ , so we need to find two numbers that add up to $-6$ and multiply to $-40$ The two numbers $-10$ and $4$ satisfy both conditions: $ {-10} + {4} = {-6} $ $ {-10} \times {4} = {-40} $ $(x {-10}) (x + {4}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -10) (x + 4) = 0$ $x - 10 = 0$ or $x + 4 = 0$ Thus, $x = 10$ and $x = -4$ are the solutions.